Question: A circle has a sector with area $90\pi$ and central angle $324^\circ$. What is the area of the circle? ${100\pi}$ $\color{#9D38BD}{324^\circ}$ ${90\pi}$
The ratio between the sector's central angle $\theta$ and $360^\circ$ is equal to the ratio between the sector's area, $A_s$ , and the whole circle's area, $A_c$ $\dfrac{\theta}{360^\circ} = \dfrac{A_s}{A_c}$ $\dfrac{324^\circ}{360^\circ} = 90\pi \div A_c$ $\dfrac{9}{10} = 90\pi \div A_c$ $A_c \times \dfrac{9}{10} = 90\pi$ $A_c = 90\pi \times \dfrac{10}{9}$ $A_c = 100\pi$